A276366 - OEIS

%I #14 Mar 10 2023 07:41:41

%S 1,1,3,12,57,300,1697,10126,62991,405247,2680901,18160444,125562250,

%T 883868590,6321838520,45869309028,337167193262,2508018933431,

%U 18861358215299,143293615189089,1098997404472941,8504070741463729,66358269984208701,521923129718567918,4136089275165532156,33013640650845937124

%N G.f. A(x) satisfies: A(x - A(x)^3) = x + A(x)^2.

%H Paul D. Hanna, <a href="/A276366/b276366.txt">Table of n, a(n) for n = 1..300</a>

%F G.f. A(x) satisfies: A'(x - A(x)^3) = (1 + 2*A'(x)*A(x)) / (1 - 3*A'(x)*A(x)^2).

%e G.f.: A(x) = x + x^2 + 3*x^3 + 12*x^4 + 57*x^5 + 300*x^6 + 1697*x^7 + 10126*x^8 + 62991*x^9 + 405247*x^10 + 2680901*x^11 + 18160444*x^12 +...

%e such that A(x - A(x)^3) = x + A(x)^2.

%e RELATED SERIES.

%e A(x - A(x)^3) = x + x^2 + 2*x^3 + 7*x^4 + 30*x^5 + 147*x^6 + 786*x^7 + 4480*x^8 + 26814*x^9 + 166865*x^10 + 1072160*x^11 + 7076724*x^12 +...

%e which equals x + A(x)^2.

%o (PARI) {a(n) = my(A=[1], F=x); for(i=1, n, A=concat(A, 0); F=x*Ser(A); A[#A] = -polcoeff(subst(F, x, x-F^3) - F^2, #A) ); A[n]}

%o for(n=1, 30, print1(a(n), ", "))

%Y Cf. A153851, A275765, A276364.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Sep 01 2016